Need Information on Router IP

[worwhite]

I'm using a broadband connection, and my ip address used to change every time
I restarted the computer. Now however, I use a router to connect 2 computers to the net, and I found that my ip address has remained the same ever since (I can't be sure that's the cause though, could be that my ISP changed it's policy or something).

What I want to ask is that does both computers (connected to the router) have the same ip address, or is there some master ip address associated with the router (how does the router change/manage IP addresses)?

Also, is my computer now more vulnerable due to the ip address being fixed now? If so, is there a solution (perhaps a software to change my ip address every time I restart)?

Thanks.

[snowmonkey]

Let me answer the last question first.

Your computer is less vulnerable if you have a router because by default all the routers are acting as firewall.

If you are using DSL connection then your routers external IP address will change every time you power it down but if you are using Cable broadband then you IP address would tend to stay the same (for a long time). IP addresses are handed out to the router by your ISP's DHCP server and, usually all the DHCP server have a lease time for IP addresses (usually 72 Hours)... Here is the what makes the DHCP server give your router a same IP address... they call it MAC address...EVERY network device (Router, PCMCIA, PC network card) has a unique MAC address that means there aren'ts two device in the world having the same REAL STATIC IP Address from their ISP (please do not confuse it with Internal IP address).

There is a lot more into the DHCP server then what I have mention
http://www.dhcp-handbook.com/dhcp_faq.html

Cheers